Consider the relation refrig(model#, year, price, manuf_plant, color),which is abbreviated as refrig(m, y, p, mp, c), and the following set f of functional dependencies: f = {m ? mp,{m, y} ? p, mp ? c}
a. evaluate each of the following as a candidate key for refrig, giving reasons why it can or cannot be a key: {m}, {m, y}, {m, c}.
b. based on the above key determination, state whether the relation refrig is in 3nf and in bcnf, giving proper reasons.
c. consider the decomposition of refrig into d = {r1(m, y, p), r2(m, mp, c)}
1. is this decomposition lossless? show why.
2. is this decomposition has the dependency preservation property?